Questions and Answers of Schaum S Outline Of Electric Circuits

Obtain the natural frequencies of the network shown in Fig. 8-26 by driving it with a conveniently located current source. 310 HE 2/5 $20 4s
The pole-zero plot in Fig. 8-39 shows a pole at s = 0 and zeros at s = −50 ± j50. Use the geometrical method to evaluate the transfer function at the test point j100. k=2 -50 1 ja,
Repeat Problem 8.17, now driving the network with a conveniently located voltage source.Data from Problem 8.17Obtain the natural frequencies of the network shown in Fig. 8-26 by driving it with a
A 5000-rad/s sinusoidal source, V = 100 ∠0° V in phasor form, is applied to the circuit of Fig. 8-27.Obtain the magnitude-scaling factor Km and the element values which will limit the current to
In the network shown in Fig. 8-40, the switch is closed at t = 0. At t = 0+, i = 0 andObtain the natural frequencies and the complete current, i = in + i=f . di dt = 25 A/s
A two-branch parallel circuit has a resistance of 20 Ω in one branch and the series combination of R = 10 Ω and L = 0.1 H in the other. First, apply an excitation, Ii(s), and obtain the natural
Refer to Fig. 8-28. Obtain H(s) = Vo/Vi for s = j4 × 106 rad/s. Scale the network with Km = 10−3 and compare H(s) for the two networks. + w 2 ΚΩ W 2 ΚΩ 0.5 mH 0.5 mH V
In the circuit of Fig. 8-41 let R1C1 = R2C2 = 10−3 s. Find v2 for t > 0 if:(a) v1 = cos(1000t)u(t),(b) v1 = sin(1000t)u(t). 사 +1 R2 W R₁ A B C2 |
A series RLC circuit contains R = 1 Ω, L = 2 H, and C = 0.25 F. Simultaneously apply magnitude and frequency scaling, with Km = 2000 and Kf = 104. What are the scaled element values?
In the circuits of Fig. 8-43(a) and 8-43(b) find the relationship between v2 and v1. 21 R R www R ww + + 2/2
A three-element series circuit contains R = 5Ω, L = 4 H, and C = 3.91 mF. Obtain the series resonant frequency, in rad/s, and then frequency-scale the circuit with Kf = 1000. Plot |Z(w)| for both
In the circuit of Fig. 8-42 assume R = 2 kΩ, C = 10 nF, and R2 = R1 and v1 = cos ωt. Find v2 for the following frequencies:(a) ω0 = 5 × 104 rad/s,(b) ω1 = 105 rad/s.
At a certain frequency ω1, a voltage V1 = 25 ∠0°V applied to a passive network results in a current I1 = 3.85 ∠−30° (A). The network elements are magnitude-scaled with Km = 10. Obtain the
In the circuit of Fig. 8-44 find the relationship between v2 and v1. Show that for R1C1 = R2C2 we obtain v2 = R2v1/(R1 + R2). + 1 0=1 ота R₁ HE C₁ R₂
In the circuit of Fig. 8-44 let R1 = 9kΩ = 9R2, C2 = 100 pF = 9C1, and v1 = 104 t V. Find i at 1 ms after the switch is closed. 1+ 0=1 ота R₁ C₁ R₂
The circuit of Fig. 8-45(a) is called a lead network.(a) Find the differential equation relating v2 to v1.(b) Find the unit-step response of the network with R1 = 10 kΩ, R2 = 1 kΩ, and C = 1
In the circuit of Fig. 8-46 find the relationship between v2 and v1 for(a) k = 103,(b) k = 105. In each case find its unit-step response; that is, v2 for v1 = u(t). U 1kΩ 1ΜΩ - 10 ΚΩ www 25
The circuit of Fig. 8-45(b) is called a lag network.(a) Find the differential equation relating v2 to v1.(b) Find the unit-step response of the network with R1 = 10 kΩ, R2 = 1 kΩ, and C = 1 μF.(c)
A 10-mH inductor has current i = 5.0 cos 2000t (A). Obtain the voltage vL.
A series circuit, with R = 10 Ω and L = 20 mH, has current i = 2.0 sin 500t (A). Obtain total voltage v and the angle by which i lags v.
Two circuit elements in a series connection have current and total voltageIdentify the two elements. i = 13.42 sin (500t - 53.4°) (A) v= 150 sin (500t +10°) (V)
The RL series circuit shown in Fig. 9-2 has a current i = I sin ω t. Obtain the voltage v across the two circuit elements and sketch v and i. R L UR UL V
An amplitude and phase angle of 10 √2 ∠45° V has an associated complex frequency s = −50 + j 100s−1.Find the voltage at t = 10 ms.
Give the complex frequencies associated with the current i(t) = 5.0 + 10e−3t cos (50t + 90°) (A).
For the three-element series circuit in Fig. 9-39,(a) Find the current I;(b) Find the voltage across each impedance and construct the voltage phasor diagram which shows that V1 + V2 + V3 = 100
Find Z in the parallel circuit of Fig. 9-41, if V = 50.0 ∠30.0° V and I = 27.9 ∠57.8° A. z US: 3 Ω -j4 Ω
Suppose that the phasor voltage across ZB, with polarity as indicated in Fig. 9-13, is sought. Choosing meshes as in Fig. 9-12 would entail solving for both I1 and I2, then obtaining the voltage as
A two-element series circuit has voltage V = 240 /0° V and current I = 50 /−60° A. Determine the current which results when the resistance is reduced to(a) 30 percent,(b) 60 percent, of its
A series RC circuit, with R = 10 Ω, has an impedance with an angle of −45° at f1 = 500 Hz. Find the frequency for which the magnitude of the impedance is(a) Twice that at f1,(b) One-half that
A practical coil is connected in series between two voltage sources v1 = 5 cosω1t and v2 = 10 cos(ω2t + 60°) such that the sources share the same reference node. See Fig. 9-54. The voltage
Determine the impedance of the series RL circuit, with R = 25 Ω and L = 10 mH, at(a) 100 Hz,(b) 500 Hz,(c) 1000 Hz.
Determine the circuit constants of a two-element series circuit if the applied voltageresults in a current i = 3.0 sin (5000t − 15°) (A). v = 150 sin (5000t + 45°) (V)
For the circuit shown in Fig. 9-18, obtain Zeq and compute I. 1000 v ( + ] U 10/0° Q 4.47/63.4° U
Evaluate the impedance Z1 in the circuit of Fig. 9-19. 2.5/-15° A 5.0 + j8.0 Ω 50/45° V Z₁
A series circuit of R = 10 Ω and C = 40 mF has an applied voltage v = 500 cos (2500t − 20°) (V). Find the resulting current i.
Compute the equivalent impedance Zeq and admittance Yeq for the four-branch circuit shown in Fig. 9-20. + V j5 2 5 0 j8.66 2 0 .. 15 Ո 2 | —j10 2
Three impedances are in series: Z1 = 3.0 ∠45° Ω, Z2 = 10 √2 ∠ 45° Ω, Z3 = 5.0 ∠− 90° Ω. Find the applied voltage V, if the voltage across Z1 is 27.0 ∠−10° V.
In the circuit of Fig. 9-55, v1 = V1 cos (t + θ1) and v2 = V2 cos (t + θ2). Find vA. +1 6 H ooo 000 0.5 F 1 F 4 H 1+ V2
A voltage transient, 35e−500t (V), has the value 25 V at t1 = 6.73 × 10−4 s. Show that at t = t1 + τ the function has a value that is 36.8 percent of that at t1.
In Fig. 7-31, the switch is closed at t = 0. Obtain the current i and capacitor voltage vC, for t > 0. 50 V + 10 Ω 10 Ω Ve 2 μF
Find the relationship between v2 and v1 in the circuit of Fig. 7-45(a). +1 R www D B w R
Find v in the circuit of Fig. 5-36. S +1 R=R A Dt 03 +1 บ
Let the circuit of Fig. 5-14 have four input lines with all values given in kΩ. The input lines are set either at 0 or 1 V. Find vo in terms of v4, v3, v2, v1, given the following sets of
Repeat Problem 5.45 forData from Problem 5.45Find v2 in the leaky integrator of Fig. 5-24 with R1 = Rf = 1 kΩ, C = 1 μF, and [1V 0 0₁ = 10 Ans. V₂(t)= -10001 (V) 1>0 1
Show that the tangent to the graph of e−t/τ at t = 0 intersects the t axis at t = t as shown in Fig. 6-12. 1 0.368 0.135 v(t) = e=1/₁ C B T 15 D t
Plot v(t) = 5 cos ω t versus ω t.
At t = 0−, just before the switch is closed in Fig. 7-20, vC = 100 V. Obtain the current and charge transients. PC 40 μF UR 400 n
A binary signal v(t) is either at 0.5 or −0.5 V. It can change its sign at 1-ms intervals. The sign change is not known a priori, but it has an equal chance for positive or negative values.
The voltage across a 1-μF capacitor is 10 V for t < 0. At t = 0, a 1-MΩ resistor is connected across the capacitor terminals. Find the time constant τ, the voltage v(t), and its value at t = 5 s.
The capacitor in the circuit shown in Fig. 7-37 has initial charge Q0 = 800 μC, with polarity as indicated. If the switch is closed at t = 0, obtain the current and charge, for t > 0. 100 V (+ 10
A 5-μF capacitor with an initial voltage of 4 V is connected to a parallel combination of a 3-kΩ and a 6-kΩ resistor (Fig. 7-2). Find the current i in the 6-kΩ resistor. σΚΩ t=0 5 με · 3
A 2-μF capacitor, with initial charge Q0 = 100 μC, is connected across a 100-Ω resistor at t = 0. Calculate the time in which the transient voltage across the resistor drops from 40 to 10 volts.
In Problem 7.1, obtain the power and energy in the resistor, and compare the latter with the initial energy stored in the capacitor.Data from Problem 7.1At t = 0−, just before the switch is closed
In the RC circuit shown in Fig. 7-38, the switch is closed on position 1 at t = 0 and then moved to 2 after the passage of one time constant. Obtain the current transient for(a) 0 (b) t > τ. 50
A 4-μF capacitor with an initial voltage of v(0−) = 2 V is connected to a 12-V battery through a resistor R = 5 kΩ at t = 0. Find the voltage across and current through the capacitor for t > 0.
The 12-V battery in Fig. 7-6(a) is disconnected at t = 0. Find the inductor current and voltage v for all times. 12 V t=0 S otos 4 Ω www 0.1 H న 10 Q2 Ω
The switch in the RL circuit shown in Fig. 7-21 is moved from position 1 to position 2 at t = 0. Obtain vR and vL with polarities as indicated. 2 A UR UL 100 2 4 H
A 10-μF capacitor, with initial charge Q0, is connected across a resistor at t = 0. Given that the power transient for the capacitor is 800e−4000t (W), find R, Q0, and the initial stored energy in
Find i, v, and i1 in Fig. 7-11(a). 9u(t) 12 Ω 60 5+ V 103 B 5 mH
For the transient of Problem 7.4 obtain pR and pL.Data from problem 7.4The switch in the RL circuit shown in Fig. 7-21 is moved from position 1 to position 2 at t = 0. Obtain vR and vL with
A series RL circuit, with R = 10 Ω and L = 1 H, has a 100-V source applied at t = 0. Find the current for t > 0.
In Fig. 7-12 the 9-μF capacitor is connected to the circuit at t = 0. At this time, capacitor voltage is v0 = 17 V. Find vA, vB, vC, iAB, iAC, and iBC for t > 0. VA A • 3 ΚΩ ww 2
In Fig. 7-39, the switch is closed on position 1 at t = 0, then moved to 2 at t = 1 ms. Find the time at which the voltage across the resistor is zero, reversing polarity. 50 V (+ +50 V 500 Ω 0.2 H
Obtain the current i, for all values of t, in the circuit of Fig. 7-23. 10 2 50 u(t) (V) |3 10 Ո 0.2 H 2u(−t) (A)
Find i and v in the circuit of Fig. 7-14. 36u(t) 3 ΚΩ ww 2 ΚΩ υ + τ 6ΚΩ 9 μF Μ 4 ΚΩ 12 ΚΩ
Find the steady-state values of iL, vC1, and vC2 in the circuit of Fig. 7-13(a). is(t)=( 34(1-1) UC R C ww 3 ΚΩ vs(t)=18u(t) ww 2 ΚΩ σΚΩ ΠΕ UCI C₁ i 4 ΚΩ www 12 ΚΩ
The switch in the circuit shown in Fig. 7-22(a) is closed at t = 0, at which moment the capacitor has charge Q0 = 500 μC, with the polarity indicated. Obtain i and q, for t > 0, and sketch the
In Fig. 7-39, the switch is closed on position 1 at t = 0, then moved to 2 at t = 1 ms. Find the time at which the voltage across the resistor is zero, reversing polarity. 50 V (+ +50 V 500 Ω 0.2 H
A series RC circuit with R = 5 kΩ and C = 20 μF has a constant-voltage source of 100 V applied at t = 0; there is no initial charge on the capacitor. Obtain i, vR, vC, and q, for t > 0.
The circuit of Problem 7.31 has a 50-V source of opposite polarity switched in at t = 0.50 ms, replacing the first source. Obtain the current for(a) 0 < t < 0.50 ms,(b) t > 0.50 ms.Data from
In Fig. 7-15(a) the switch S is closed at t = 0. Find i and v for all times. 12 V + 1 S 1=0 www ΖΩ 6Ω www 3 Ω + υ 100 mH
In Fig. 7-24(a), the switch is closed at t = 0. The capacitor has no charge for t r, ic, vC, and vs for all times if is = 2 mA. i,=2 mA (4 V₂ t=0 + UC tic 2 μF İR 5 5 ΚΩ
Find i and v for t = 0− and t = 0+ in the circuit of Fig. 7-16, given R = 5 Ω, L = 10 mH, and V₂ = [5V [5 sin cot (V) for t < 0 for t > 0
In Fig. 7-25, the switch is opened at t = 0. Find iR, iC, vC, and vs. 6 mA ↑ Us • 4 ΚΩ 1=0 VC ic 2 μF · 3 ΚΩ iR 2 ΚΩ
A transient that increases from zero toward a positive steady-state magnitude is 49.5 at t1 = 5.0 ms, and 120 at t2 = 20.0 ms. Obtain the time constant τ.
In the circuit of Fig. 7-17(a), let R = 1 kΩ and C = 1 μF and let the voltage source be a pulse of height V0 and duration T. Find i and v for(a) V0 = 1 V and T = 1 ms, (b) V0 = 10 V and T = 0.1
The circuit shown in Fig. 7-40 is switched to position 1 at t = 0, then to position 2 at t = 3τ. Find the transient current i for(a) 0 (b) t > 3τ. 25 V (+ 0,5 με 2 Τ ΤΟ Ω 1.5 με 5 Ω 2
The switch in the circuit of Fig. 7-26 is closed on position 1 at t = 0 and then moved to 2 after one time constant, at t = τ = 250 μs. Obtain the current for t > 0. 20 V (+ 2 40 V Uc 500 0.5 μF
A series RL circuit has a constant voltage V applied at t = 0. At what time does vR = vL?
Find the limits of i and v of the circuit in Fig. 7-17(a) for a voltage pulse of unit area as the pulse duration is decreased to zero. V, Vo[u(1)-u(t-T)]( R www C
Find the impulse responses of the RC circuit in Fig. 7-17(a) by taking the derivatives of its unit step responses. v₁= Volu(1) - u(t-T)]( R C V
An RL circuit, with R = 300 Ω and L = 1 H, has voltage v = 100 cos (100t + 45°) (V) applied by closing a switch at t = 0. [A convenient notation has been used for the phase of v, which, strictly
A constant voltage is applied to a series RL circuit at t = 0. The voltage across the inductance is 20 V at 3.46 ms and 5 V at 25 ms. Obtain R if L = 2h.
The RC circuit shown in Fig. 7-41 has an initial charge on the capacitor Q0 = 25 μC, with polarity as indicated. The switch is closed at t = 0, applying a voltage v = 100 sin (1000t + 30°) (V).
In Fig. 7-28, switch S1 is closed at t = 0. Switch S2 is opened at t = 4 ms. Obtain i for t > 0. 100 V (+ S₁ 50 Ω U 100 Ω • Η ΤΟ Sz
Find the impulse responses hi(t), hv(t), and hi1(t) of the RL circuit of Fig. 7-11(a) by taking the derivatives of its unit step responses. 9u(1) 12 Ω 6Ω e 183 B 5 mH
What initial charge on the capacitor in Problem 7.37 would cause the current to go directly into the steady state without a transient?Data from problem 7.37The RC circuit shown in Fig. 7-41 has an
In the circuit of Fig. 7-29, the switch is closed at t = 0, when the 6-μF capacitor has charge Q0 = 300 μC.Obtain the expression for the transient voltage vR. 6 μF 20 Ω + UR 1 μF 2 μF
The op amp in the circuit of Fig. 7-44 is ideal. Find the unit-step response of the circuit; that is, v2 for v1 = u(t). VI +1 с + Vc - A R₁ www + R₂ U₂ "2
Write simultaneous differential equations for the circuit shown in Fig. 7-42 and solve for i1 and i2. The switch is closed at t = 0 after having been open for an extended period of time. 100 V
In the circuit shown in Fig. 7-30, the switch is moved to position 2 at t = 0. Obtain the current i2 at t = 34.7 ms. 6 A 2 200 Ω www 5 H 10 H
In the circuit of Fig. 7-44 derive the differential equation relating v2 to v1. Find its unit-step response and compare with the answer in Example 7.15.Data from Example 7.15The op amp in the circuit
For the RL circuit shown in Fig. 7-43, find the current iL at the following times:(a) −1 ms,(b) 0+,(c) 0.3 ms,(d) ∞. 50u(t) (V) (+ 20 Ω 30) Ω 10 mH IS A
The switch in the two-mesh circuit shown in Fig. 7-32 is closed at t = 0. Obtain the currents i1 and i2 for t > 0. 100 V (+ 10 Ω •Σ 5 Ω 0.01 Η ܕܐ 351 Ω
Show that the relationship between v2 and v1 in the circuit of Fig. 7-45(b) is the same as in Fig. 7-45(a). HH R M D B - + w R R₁ www www R B (b) R₁ V/2
A series RC circuit, with R = 2 kΩ and C = 40 μF, has two voltage sources in series with each other, v1 = 50 V and v2 = −100u(t) (V). Find(a) The capacitor voltage at t = τ,(b) The time at
Find the unit-impulse response of the circuit of Fig. 7-44; i.e., v2 for v1 = δ(t) (a unit-area narrow voltage pulse). VI с HH + Ve A R₁ www + R₂ D₂ =
A series RL circuit, with R = 50 Ω and L = 0.2 H, has a sinusoidal voltageapplied at t = 0. Obtain the current for t > 0. v= 150 sin (500t + 0.785) (V)
In the circuits of Fig. 7-45, RC = 5 × 10−7 and v1(t) = 10 + cos (1000t) + 3 cos (2000t). Find v2(t). Assume tan θ ≈ θ when θ R W D B 3 R O 2/₁ R₁ R B (b) R₁ ww V/₂
For the circuit of Fig. 7-33, obtain the current iL for all values of t. (V) (+ 50 u(-1) (V) 10 f 0.2 mH İL 10 Ω t. 5 u(t) (A)

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